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February, 1978 An Extended Martingale Invariance Principle
D. L. McLeish
Ann. Probab. 6(1): 144-150 (February, 1978). DOI: 10.1214/aop/1176995619


In this note the conditions on an invariance principle for triangular arrays of random variables contained in an earlier paper are weakened. Random norming by functions which are not stopping times is permitted, the $L^2$-boundedness conditions on the maximum of the summands relaxed, and joint convergence with an arbitrary sequence of random elements of some other metric space proved.


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D. L. McLeish. "An Extended Martingale Invariance Principle." Ann. Probab. 6 (1) 144 - 150, February, 1978.


Published: February, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0379.60046
MathSciNet: MR471032
Digital Object Identifier: 10.1214/aop/1176995619

Primary: 60F05
Secondary: 60G45

Keywords: central limit theorem , Donsker's theorem , invariance principle , Martingales

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 1 • February, 1978
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